Data quality assessment has become a prominent component in the successful execution of complex data-driven artificial intelligence (AI) software systems. In practice, real-world applications generate huge volumes of data at speeds. These data streams require analysis and preprocessing before being permanently stored or used in a learning task. Therefore, significant attention has been paid to the systematic management and construction of high-quality datasets. Nevertheless, managing voluminous and velocious data streams is usually performed manually (i.e., offline), making it impractical strategy in production environments. To address this challenge, DataOps has emerged to achieve life-cycle automation of data processes using DevOps principles. However, determining the data quality based on a fitness scale constitutes a complex task within the framework of DataOps. This paper presents a novel Data Quality Scoring Operations (DQSOps) framework that yields a quality score for production data in DataOps workflows. The framework incorporates two scoring approaches, an ML prediction-based approach that predicts the data quality score and a standard-based approach that periodically produces the ground-truth scores based on assessing several data quality dimensions. We deploy the DQSOps framework in a real-world industrial use case. The results show that DQSOps achieves a significant computational speedup rates compared to the conventional approach of data quality scoring while maintaining high prediction performance.